障碍体和凹凸体对地震矩的影响
EFFECTS OF BARRIERS AND ASPERITIES ON SEISMIC MOMENT
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摘要: 本文利用具有非均匀剪切应力分布的圆盘状裂缝问题的解,定量计算了障碍体和凹凸体对地震矩的影响.我们发现,除非障碍体的尺寸很小或很接近于整个断层的尺寸,含有障碍体的断层的地震矩,大致为具有均匀应力降的等面积断层的地震矩的40%.由此可以推知,在障碍体的这种尺寸范围内,视应力降大致也是△Af=SA-f的40%.这里SA是远场应力,f是残余摩擦应力.另外,已存在滑动带对于凹凸体破坏的地震矩有明显的放大作用,这种作用在凹凸体尺寸较小时特别显著.例如,当凹凸体半径是整个断层半径的2/10时,凹凸体上的矩被放大7倍多;当其半径为整个断层半径的1/10时,凹凸体的矩将被放大约30倍. 文中还比较了三维效应和二维效应的差异.我们发现,Mx0/M0c在三维情形对障碍体尺寸的变化并不敏感,这是与二维情形很不相同的.这里,Mx0是具有障碍体的断层破裂所产生的地震矩,M0c是相应的均匀断层破裂的矩.所以,二维分析不适用于具有障碍体的三维断层.然而,在分析已存在滑动带对凹凸体破裂的矩的影响时,平面应变结果与三维结果差异并不很大.Abstract: In this paper,the effects of barriers and asperities on the determination of seismic moment have been quantitatively examined by using the solution for a penny-shaped crack with non-uniform traction. It has been found that the moment of a fault with a barrier is about 40 percent of the moment on the fault with uniform stress drop and the same area,if the radius of the barrier is not very small,nor approximates to that of the fault. Therefore,it follows that,in this case,the apparent stress drop is about 40 percent of △Af=SA-f where SA is the far-field stress and f is the uniform residual frictional stress. Furthermore,a pre-existing slip zone can substantially amplify the seismic moment due to the failure of an asperity. Especially,the amplification is very large when the radius of the asperity is small. For example,the moment on the asperity is over 7 times and 30 times of the moment at the failure of a uniform shear fault with radius C,respectively,when the radius of the asperity is 20 percent and 10 percent of the radius C of the fault.The difference between three-dimensional and two-dimensional effects is compared in this paper. It is founl that Mx0/M0c is not sensitive to the change of asperity radius for three-di-mensionad faults,this differs very mith from the result with two-dimensional fault,where Mx0 is the moment due to the failure of the fault with an asperity and M0c is the moment of a uniform fault. Therefore,two-dimensional analsis is not suitable to a three-dimensional fault with asperity. However,when examining the effect of pre-existing slip zones on the moment due to failure of asperity,the difference between the results of plane strain and three-dimensional case is not apparent.